A291765 Compound filter (sum of proper divisors & prime signature): a(n) = P(A001065(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 2, 18, 2, 61, 2, 98, 25, 86, 2, 367, 2, 115, 100, 450, 2, 517, 2, 550, 131, 185, 2, 1747, 42, 226, 203, 769, 2, 2527, 2, 1922, 205, 320, 166, 4060, 2, 373, 248, 2678, 2, 3457, 2, 1315, 979, 491, 2, 7579, 63, 1474, 346, 1642, 2, 3982, 248, 3805, 401, 698, 2, 13969, 2, 775, 1367, 7938, 295, 5749, 2, 2404, 523, 5327, 2, 18844, 2, 1030, 1819, 2839, 295

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16385

Formula

a(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n)).

Prog

(PARI)
A001065(n) = (sigma(n)-n);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));

Crossrefs

Cf. A000027, A000203, A001065, A046523, A286360, A286592.

Sequence in context: A260478 A074970 A297794 * A231123 A225123 A087338

Adjacent sequences: A291762 A291763 A291764 * A291766 A291767 A291768

Keyword

nonn

Author

Antti Karttunen, Sep 10 2017

Status

approved